Answer:
E. 7/40
Step-by-step explanation:
The following probabilities are given:
P (Alice Wins) = 1/5
P (Benj. Wins) = 3/8
P (Carol Wins) = 2/7
We can deduce the probabilities for losses:
P (Alice Loses) = 1 - P (Alice Wins) = 1 - 1/5 =4/5
P (Benj. Loses) = 1 - P (Benj. Wins) = 1 - 3/8 = 5/8
P (Carol Loses) = 1 - P (Carol Wins) = 1 - 2/7 =5/7
The possible outcomes that two players win and one player loses are as follows:
Alice Wins, Benj Wins, Carol Loses
Alice Loses, Benj Wins, Carol Wins
Alice Wins, Benj Loses, Carol Wins
We can compute the probabilities of each of the 3 outcomes above:
P(Alice Wins, Benj Wins, Carol Loses) = (1/5) x (3/8) x (5/7) = 3/56
Alice Loses, Benj Wins, Carol Wins = (4/5) x (3/8) x (2/7) = 3/35
Alice Wins, Benj Loses, Carol Wins = (1/5) x (5/8) x (2/7) = 2/56
P ( 2 wins and 1 loss)
= 3/56 + 3/35 + 2/56
= 343 / 1960
= 7/40
